Algebraic Riccati equation

An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time or discrete time. A typical algebraic Riccati equation is similar to one of the following: the continuous time algebraic Riccati equation (CARE): A ⊤ P + P A − P B R − 1 B ⊤ P + Q = 0 {\displaystyle A^{\top }P+PA-PBR^{-1}B^{\top }P+Q=0} or the discrete time algebraic Riccati equation (DARE): P = A ⊤ P A − ( A ⊤ P B ) ( R + B ⊤ P B ) − 1 ( B ⊤ P A ) + Q .

Source: Wikipedia — Algebraic Riccati equation (CC BY-SA 4.0)